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The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the…

General Mathematics · Mathematics 2009-12-31 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

Given a nonempty set $X$ and a function $f:X \rightarrow X$, three fuzzy topological spaces are introduced. Some properties of these spaces and relation among them are studied and discussed.

General Mathematics · Mathematics 2017-02-07 Ismael Akray

This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter…

General Mathematics · Mathematics 2010-03-10 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or…

General Mathematics · Mathematics 2010-12-14 W. B. Vasantha Kandasamy , Florentin Smarandache

In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is…

General Mathematics · Mathematics 2008-06-18 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

The major part of this thesis deals with fuzzy geometric logic and fuzzy geometric logic with graded consequence. The first chapter mainly contains the concept of topological system introduced by S. Vickers in 1989. In Chapter 2 the notion…

General Mathematics · Mathematics 2017-05-16 Purbita Jana

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational…

General Mathematics · Mathematics 2008-01-18 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Amal

The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white. This…

General Mathematics · Mathematics 2007-05-23 Dr. W. B. Vasantha Kandasamy

In this article we compute the number of fuzzy bitopological space with having two open sets, three open sets, four open sets and five open sets. Also, we have given some results on computation of number of fuzzy bitopological space.

General Topology · Mathematics 2019-12-10 Bhimraj Basumatary , Jili Basumatary , Nijwm Wary

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of fuzzy spaces. Dip's approach helps to rectify the deviation in some definitions of fuzzy subsets in fuzzy topological spaces. In this paper, further…

General Topology · Mathematics 2021-05-18 Abd Ulazeez Alkouri , Mohammad Hazaimeh , Ibrahim Jawarneh

In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval…

General Mathematics · Mathematics 2011-02-11 W. B. Vasantha Kandasamy , Florentin Smarandache

This is a preliminary version, comments and inputs are welcome. Contents: 1. Introduction. 2. Fuzzy Spaces. 3. Star Products. 4. Scalar Fields on the Fuzzy Sphere. 5. Instantons, Monopoles and Projective Modules. 6. Fuzzy Nonlinear Sigma…

High Energy Physics - Theory · Physics 2007-05-23 A. P. Balachandran , S. Kurkcuoglu , S. Vaidya

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…

Functional Analysis · Mathematics 2017-03-01 Murat Kirişci

This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three…

General Mathematics · Mathematics 2011-06-06 W. B. Vasantha Kandasamy , Florentin Smarandache

This is a book about large language models. As indicated by the title, it primarily focuses on foundational concepts rather than comprehensive coverage of all cutting-edge technologies. The book is structured into five main chapters, each…

Computation and Language · Computer Science 2025-06-17 Tong Xiao , Jingbo Zhu

In this paper, three topics in bipolar fuzzy soft hypervector spaces are investigated. At first, four equivalent conditions to definition of a bipolar fuzzy soft hypervector space are presented, from different point of views. Then some new…

General Mathematics · Mathematics 2023-10-12 O. R. Dehghan

B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and…

General Mathematics · Mathematics 2012-03-21 J. Mahanta , P. K. Das

For the past few decades, man has been trying to create an intelligent computer which can talk and respond like he can. The task of creating a system that can talk like a human being is the primary objective of Automatic Speech Recognition.…

Artificial Intelligence · Computer Science 2012-09-21 Sachin Lakra , T. V. Prasad , Deepak Kumar Sharma , Shree Harsh Atrey , Anubhav Kumar Sharma

The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache

Conceptual formalism supported by typical ontologies may not be sufficient to represent uncertainty information which is caused due to the lack of clear cut boundaries between concepts of a domain. Fuzzy ontologies are proposed to offer a…

Artificial Intelligence · Computer Science 2018-05-08 Zahra Riahi Samani , Mehrnoush Shamsfard
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